The text of these chapters is found in the Septuagint, the earliest extant Greek translation of the Hebrew Bible from the original Hebrew.
The Book of Daniel is preserved in the 12-chapter Masoretic Text and in two longer Greek versions: the original Septuagint version, c. 100 BCE, and the later Theodotion version from c. 2nd century CE.
Both Greek texts contain the three additions to Daniel.
In other respects Theodotion is much closer to the Masoretic Text, and became so popular that it replaced the original Septuagint version in all but two manuscripts of the Septuagint itself.
[4][5][6] The Greek additions were apparently never part of the Hebrew text.